Randomness and Probability

Solomon Bt, Beckwith Aw

Quantum theory does not have a mechanism that explains how nature implements probabilities. Thus, the main objective of this paper is to present new directions in the understanding of probabilities and randomness with the eventual objective of controlling photon localization (in a future paper). The expectation is to improve photon collection and loss mitigation. The conservation of energy within the photon’s transverse electromagnetic wave requires that energy is transferred between spacetime (x,y,z,t) and subspace (x,y,z). This paper proposes that it is in this subspace that nature implements probabilities. The paper analyses the differences between probabilities and randomness and infers that all particles have internal clocks C, that is the mechanism for randomness. A glass thought experiment is used to clarify how probabilities are effected and as a result it is proposed that the random distribution of photons across the Point Spread Function or Airy Pattern (not Airy Disc) is not due to the photon probability but due to the random behaviour of electron shells receiving the photon localization. Finally, 5 experiments are proposed.

Roman Frič, Martin Papčo

The influence of “Grundbegriffe” by A. N. Kolmogorov (published in 1933) on education in the area of probability and its impact on research in stochastics cannot be overestimated. We would like to point out three aspects of the classical probability theory “calling for” an upgrade: (i) classical random events are black-and-white (Boolean); (ii) classical random variables do not model quantum phenomena; (iii) basic maps (probability measures and observables { dual maps to random variables) have very different “mathematical nature”. Accordingly, we propose an upgraded probability theory based on Łukasiewicz operations (multivalued logic) on events, elementary category theory, and covering the classical probability theory as a special case. The upgrade can be compared to replacing calculations with integers by calculations with rational (and real) numbers. Namely, to avoid the three objections, we embed the classical (Boolean) random events (represented by the f0; 1g-valued indicator functions of sets) into upgraded random events (represented by measurable {0; 1}-valued functions), the minimal domain of probability containing “fractions” of classical random events, and we upgrade the notions of probability measure and random variable.

A. Biryukov

Abstract The evolution of the system is described as a stochastic process in the space of random joint events. A symmetric difference and a symmetric sum of random joint events are introduced in space. The probability of quantum transitions of the system between certain random events is represented by the sum of the probabilities of joint events (two, three, … ). It is noteworthy that the obtained expression for the transition probabilities coincides with the transition probability in quantum theory, if only pairwise joint random events are taken into account in the model.

Clas Blomberg